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Ambiguity attitudes and self-confirming equilibrium in sequential games

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  • Battigalli, P.
  • Catonini, E.
  • Lanzani, G.
  • Marinacci, M.

Abstract

We consider a game in extensive form recurrently played by agents who are randomly drawn from large populations and matched. We assume that preferences over actions at any information set admit a smooth-ambiguity representation in the sense of Klibanoff et al. (2005), which may induce dynamic inconsistencies. We take this into account in our analysis of self-confirming equilibrium (SCE) given players' feedback about the path of play. Battigalli et al. (2015) show that the set of SCE's of a simultaneous-move game with feedback expands as ambiguity aversion increases. We show by example that SCE in a sequential game is not equivalent to SCE applied to the strategic form of such game, and that the previous monotonicity result does not extend to general sequential games. Still, we provide sufficient conditions under which the monotonicity result holds for SCE.

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  • Battigalli, P. & Catonini, E. & Lanzani, G. & Marinacci, M., 2019. "Ambiguity attitudes and self-confirming equilibrium in sequential games," Games and Economic Behavior, Elsevier, vol. 115(C), pages 1-29.
    • Handle: RePEc:eee:gamebe:v:115:y:2019:i:c:p:1-29
    DOI: 10.1016/j.geb.2019.02.005
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    Cited by:

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    2. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    3. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    4. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    5. Battigalli, P. & Catonini, E. & Lanzani, G. & Marinacci, M., 2019. "Ambiguity attitudes and self-confirming equilibrium in sequential games," Games and Economic Behavior, Elsevier, vol. 115(C), pages 1-29.
    6. Eran Hanany & Peter Klibanoff & Sujoy Mukerji, 2020. "Incomplete Information Games with Ambiguity Averse Players," American Economic Journal: Microeconomics, American Economic Association, vol. 12(2), pages 135-187, May.
    7. Auster, Sarah & Kellner, Christian, 2022. "Robust bidding and revenue in descending price auctions," Journal of Economic Theory, Elsevier, vol. 199(C).
    8. Chen, Jaden Yang, 2022. "Biased learning under ambiguous information," Journal of Economic Theory, Elsevier, vol. 203(C).
    9. Li, Chen & Turmunkh, Uyanga & Wakker, Peter P., 2020. "Social and strategic ambiguity versus betrayal aversion," Games and Economic Behavior, Elsevier, vol. 123(C), pages 272-287.
    10. Tommi Ekholm & Erin Baker, 2022. "Multiple Beliefs, Dominance and Dynamic Consistency," Management Science, INFORMS, vol. 68(1), pages 529-540, January.
    11. Pierpaolo Battigalli & Nicolò Generoso, 2021. "Information Flows and Memory in Games," Working Papers 678, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    12. Battigalli, P. & Francetich, A. & Lanzani, G. & Marinacci, M., 2019. "Learning and self-confirming long-run biases," Journal of Economic Theory, Elsevier, vol. 183(C), pages 740-785.
    13. Pierpaolo Battigalli & Davide Bordoli, 2023. "Sophisticated Reasoning, Learning, and Equilibrium in Repeated Games with Imperfect Feedback," Working Papers 702, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    14. Sebastiano Della Lena & Fabrizio Panebianco, 2019. "Cultural Transmission with Incomplete Information: Parental Perceived Efficacy and Group Misrepresentation," Working Papers 2019:11, Department of Economics, University of Venice "Ca' Foscari".

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    More about this item

    Keywords

    Sequential games with feedback; Smooth ambiguity; Self-confirming equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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